Abstract
It is proved that (i) for\(p \geqslant 5,2 \leqslant s \leqslant p - 1,k \geqslant 2,\bar \beta _1 h_0 h_{k + 1} \) survives to E∞; (ii) for\(p \geqslant 7,3 \leqslant s \leqslant p - 1,k \geqslant 3,\bar \gamma _1 h_0 h_{k + 1} \) survives to E∞.
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References
Adams, J. F., On the structure and application of the Steenrod algebra,Commentarii Math. Helwtici, 1958, 32: 180.
Adams, J. F., On the non-existence of elements of Hopf invariant one,Annals of Math., 1960, 72: 20.
Liulevicius, A., The factorization of cyclic reduced powers by secondary cohornology operations.Memoirs of A. M. S., 1962, 42.
Miller, H., Ravenel, D., Wilson, W. S., Periodic phenomena in the Adams-Novikov spectral sequence,Annals of Math., 1977, 106: 469.
Ravenel, D.,Complex Coburdism and Stable Homotopy Groups of Spheres, New York: Academic Press, 1986.
Wang **angjun, Some notes on the Adams spectral sequence,Acta Math. Sinica, New series, 1994, 10(1): 4.
Cohen, R., Goerss, P., Secondary cohomology operations that detect homotopy classes,Topology, 1984, 23: 77.
Cohen, R., Odd primary infinite families in stable homotopy theory,Memoirs of A. M. S., 1981, 242.
Zhou, X., Higher cohonlology operations that detect homotopy classes, inAlgebraic Topolgy, (eds. Dold, A. B., Eckmann, G., Carlsson, R. L. etal.), New York: Springer-Verlag, 1986.
Smith, L., On realizing complex cobordism modules,American Journal of Mathematics, 1970, 92: 793.
Toda, H., On spectra realizing exterior part of the Steenrod algebra,Topology, 1971, 10: 53.
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Project supported by the Doctoral Program Foundation of China.
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Wang, X., Zheng, Q. The convergence of\(\tilde a_s^{(n)} h_0 h_k \) . Sci. China Ser. A-Math. 41, 622–628 (1998). https://doi.org/10.1007/BF02876232
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DOI: https://doi.org/10.1007/BF02876232